Nth terms' pattern pattern

Hey!
So, I kinda need some help...
I'm trying to work out the nth term of this, but it's beginning to get hard, I remember when it goes into the nth term term you need to square things, and stuff...

Code:

---

2)  100,000
          - 200,000
3)  300,000        - 100,000
          - 300,000
4)  600,000        - 100,000
          - 400,000
5)1,000,000


                        2) 50,000
                        3)100,000
                        4)150,000
                        5)200,000
                        50(n-1)

2) 50,000
3)200,000
4)450,000
5)800,000

---

-
That was just my rough working out, if you can understand any of it, a head-start. Otherwise, my pattern is

Code:

---

2)  100,000
3)  300,000
4)  600,000
5)1,000,000

---

I've forgotten how to do this, and all of the online sites are useless!
Thanks if anyone helps.

I think I may have found it.
10,000(10(n-1)) + 50(n-1)
I'm testing it now, but I think.


----


I got it!! It's:
(10000 * (10 * ($n-1)) + 50000 * ($n-1)) / 3 * 2 * ($n / 2) :afrog:

But of course you know that was using the old trial and error. I have about 30 of these to do, and trial and erro does not apply onto ones like this

Code:

---

2) 4,800
3)12,000
4)21,600
5)33,600

---

...Can someone tell me the actual way to do this please?

This might help you out:

BTW, in Step2, AX0 represents B from the Difference Pyramid.

Quote:

---

Originally Posted by CT0581

But of course you know that was using the old trial and error. I have about 30 of these to do, and trial and erro does not apply onto ones like this

Code:

---

2) 4,800
3)12,000
4)21,600
5)33,600

---

...Can someone tell me the actual way to do this please?

---

So:

Lets build a difference tree:

4800 12000 21600 33600
7200 9600 12000
2400 2400

So, as you see, the elements of a line below another line is equal to the above right number minus the above number.

And as you see, the last line contains identical elements.

So, the equation becomes:

Y = 4800 + 7200*X + 2400*X(X-1)/2
==> 4800 + 7200*X + 1200*X² - 1200*X
==> 4800 + 6000*X + 1200*X²

Or:

Y = 1200*(X² + 5*X + 4)

So, when X=0,1,2,3...:

X Y
0 4800
1 12000
2 21600
3 33600
and so on

-Lou